Solve for $x$ and $y$ using elimination. ${2x-y = 13}$ ${5x+y = 50}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $7x = 63$ $\dfrac{7x}{{7}} = \dfrac{63}{{7}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {2x-y = 13}\thinspace$ to find $y$ ${2}{(9)}{ - y = 13}$ $18-y = 13$ $18{-18} - y = 13{-18}$ $-y = -5$ $\dfrac{-y}{{-1}} = \dfrac{-5}{{-1}}$ ${y = 5}$ You can also plug ${x = 9}$ into $\thinspace {5x+y = 50}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ + y = 50}$ ${y = 5}$